MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 357 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 24 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 96 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x = x4 && 0 <= x5 && x5 <= 0 && x5 = x5 && 0 <= -1 - x2 + x3 l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 l0(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = x21 && 0 <= -1 - x18 + x19 l4(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x25 <= 0 l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x33 l5(x40, x41, x42, x43) -> l3(x44, x45, x46, x47) :|: x43 = x47 && x41 = x45 && x40 = x44 && x46 = 1 + x42 l3(x48, x49, x50, x51) -> l0(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 l6(x56, x57, x58, x59) -> l0(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 l7(x64, x65, x66, x67) -> l6(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 Start term: l7(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x = x4 && 0 <= x5 && x5 <= 0 && x5 = x5 && 0 <= -1 - x2 + x3 l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 l0(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = x21 && 0 <= -1 - x18 + x19 l4(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x25 <= 0 l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x33 l5(x40, x41, x42, x43) -> l3(x44, x45, x46, x47) :|: x43 = x47 && x41 = x45 && x40 = x44 && x46 = 1 + x42 l3(x48, x49, x50, x51) -> l0(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 l6(x56, x57, x58, x59) -> l0(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 l7(x64, x65, x66, x67) -> l6(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 Start term: l7(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 (2) l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x = x4 && 0 <= x5 && x5 <= 0 && x5 = x5 && 0 <= -1 - x2 + x3 (3) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 (4) l0(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = x21 && 0 <= -1 - x18 + x19 (5) l4(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x25 <= 0 (6) l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x33 (7) l5(x40, x41, x42, x43) -> l3(x44, x45, x46, x47) :|: x43 = x47 && x41 = x45 && x40 = x44 && x46 = 1 + x42 (8) l3(x48, x49, x50, x51) -> l0(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 (9) l6(x56, x57, x58, x59) -> l0(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 (10) l7(x64, x65, x66, x67) -> l6(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 Arcs: (2) -> (3) (3) -> (1), (2), (4) (4) -> (5), (6) (5) -> (7) (6) -> (7) (7) -> (8) (8) -> (1), (2), (4) (9) -> (1), (2), (4) (10) -> (9) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x = x4 && 0 <= x5 && x5 <= 0 && x5 = x5 && 0 <= -1 - x2 + x3 (2) l3(x48, x49, x50, x51) -> l0(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 (3) l5(x40, x41, x42, x43) -> l3(x44, x45, x46, x47) :|: x43 = x47 && x41 = x45 && x40 = x44 && x46 = 1 + x42 (4) l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x33 (5) l4(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x25 <= 0 (6) l0(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = x21 && 0 <= -1 - x18 + x19 (7) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 Arcs: (1) -> (7) (2) -> (1), (6) (3) -> (2) (4) -> (3) (5) -> (3) (6) -> (4), (5) (7) -> (1), (6) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x12:0, x1:0, x14:0, x15:0) -> l0(x12:0, x13:0, x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 l0(x16:0, x17:0, x18:0, x19:0) -> l0(x16:0, x21:0, 1 + x18:0, x19:0) :|: 0 <= -1 - x18:0 + x19:0 && x21:0 < 0 l0(x, x1, x2, x3) -> l0(x, x4, 1 + x2, x3) :|: 0 <= -1 - x2 + x3 && x4 > 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4) -> l0(x3, x4) ---------------------------------------- (8) Obligation: Rules: l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 l0(x18:0, x19:0) -> l0(1 + x18:0, x19:0) :|: 0 <= -1 - x18:0 + x19:0 && x21:0 < 0 l0(x2, x3) -> l0(1 + x2, x3) :|: 0 <= -1 - x2 + x3 && x4 > 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 l0(x18:0, x19:0) -> l0(c, x19:0) :|: c = 1 + x18:0 && (0 <= -1 - x18:0 + x19:0 && x21:0 < 0) l0(x2, x3) -> l0(c1, x3) :|: c1 = 1 + x2 && (0 <= -1 - x2 + x3 && x4 > 0) Found the following polynomial interpretation: [l0(x, x1)] = -x + x1 The following rules are decreasing: l0(x18:0, x19:0) -> l0(c, x19:0) :|: c = 1 + x18:0 && (0 <= -1 - x18:0 + x19:0 && x21:0 < 0) l0(x2, x3) -> l0(c1, x3) :|: c1 = 1 + x2 && (0 <= -1 - x2 + x3 && x4 > 0) The following rules are bounded: l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 l0(x18:0, x19:0) -> l0(c, x19:0) :|: c = 1 + x18:0 && (0 <= -1 - x18:0 + x19:0 && x21:0 < 0) l0(x2, x3) -> l0(c1, x3) :|: c1 = 1 + x2 && (0 <= -1 - x2 + x3 && x4 > 0) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 ---------------------------------------- (10) Obligation: Rules: l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x13:0 < 1 && x13:0 > -1 && 0 <= -1 - x14:0 + x15:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l0(x14:0:0, x15:0:0) -> l0(x14:0:0, x15:0:0) :|: x13:0:0 < 1 && x13:0:0 > -1 && 0 <= -1 - x14:0:0 + x15:0:0